Stock ABC and Stock XYZ have the same current price of $50, and they offer the s

Question

Stock ABC and Stock XYZ have the same current price of $50, and they offer the same distribution of future returns (with the same expected return and the same standard deviation). There exists a call option on one share of Stock ABC and a call option on one share of Stock XYZ. The options have identical exercise prices of $49 and they expire on the same date. The call premium on each option is $3. A.) Are the options currently “in” or “out” of the money? B.) What is the intrinsic value and the time value of each option today? C.) What is the break-even future stock price associated with the options? D.) What is the net profit or loss associated with purchasing either option if the future stock price is $30. E.) What is the net profit or loss associated with writing either option if the future stock price is $48? F.) What is the net profit or loss associated with writing either option if the future stock price is $51? G.)What is the net profit or loss associated with writing either option if the future stock price is $80? H.) Assume that there is a third call option, based on the average price of Stocks ABC and XYZ, with the same expiration date as the first two options. The exercise price of this option is $49. Should the price (call premium) of the third option be higher than, lower than, or equal to the prices of the two options on the individual stocks in the following two cases? (Briefly explain your answer in each case). -The correlation between the returns of the ABC and XYZ is +1 -The correlation between the returns of the two stocks is +0.3

Explanation / Answer

ANS:

A) The option is in the money option because the spot price of the stock is greater than strike price.

B) We have,

Intrinsic Value for Call Option=Underlying price-Strike price

So, For Stock ABC,

Intrinsic Value=$50-$49

=$1

For Stock XYZ,

Intrinsic Value=$50-$49

=$1

Similarly We have time value=Premium-Intrinsic Value

So, Time value for ABC=$3-$1

=$2

Time value for ABC=$3-$1

=$2

C) We have, Breakeven Price=Strike price+Premium Charges+Commision Charges

So, Breakeven Price of Stock ABC=$49+$3=$52

Breakeven Price of Stock XYZ=$49+$3=$52

D) We have,

When price is $30,The buyer of option will not exercise his right,

So Net Loss=Premim Paid=$3 (For each option)

E) When future stock price is $ 48, the buyer of option will not exercise his right, because he can buy the share from market at $ 48.,

So Net Loss=Premim Paid=$3 (For each option)

F) When future stock price will be $ 51, the buyer will exercise his right,

So Net Profit/Loss=Future Stock Price-Strike Price - Premium Paid

=$51-$49-$3

=(-)$ 1

Therefore, Net Loss=$1

G) When Future Stock Price=80,

Profit=$80-$49-$3

Therefore, Net Profit=$ 28.

H) When correlation will be 1, the stock price will be equal to the prices the two options on the individual options because when correlation will be 1, it means relationship betweenn two datra is 100% positive.

When correaltion will be .3, the stock price will lesser to the prices of two options on the individual stocks, beacause the relation betwwen two data will be 30% positive.

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